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# Collatz Conjecture | ||
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The Collatz Conjecture or 3x+1 problem can be summarized as follows: | ||
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Take any positive integer n. If n is even, divide n by 2 to get n / 2. If n is | ||
odd, multiply n by 3 and add 1 to get 3n + 1. Repeat the process indefinitely. | ||
The conjecture states that no matter which number you start with, you will | ||
always reach 1 eventually. | ||
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Given a number n, return the number of steps required to reach 1. | ||
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## Examples | ||
Starting with n = 12, the steps would be as follows: | ||
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0. 12 | ||
1. 6 | ||
2. 3 | ||
3. 10 | ||
4. 5 | ||
5. 16 | ||
6. 8 | ||
7. 4 | ||
8. 2 | ||
9. 1 | ||
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Resulting in 9 steps. So for input n = 12, the return value would be 9. | ||
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## Getting Started | ||
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For installation and learning resources, refer to the | ||
[exercism help page](http://exercism.io/languages/haskell). | ||
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## Running the tests | ||
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To run the test suite, execute the following command: | ||
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```bash | ||
stack test | ||
``` | ||
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#### If you get an error message like this... | ||
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``` | ||
No .cabal file found in directory | ||
``` | ||
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You are probably running an old stack version and need | ||
to upgrade it. | ||
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#### Otherwise, if you get an error message like this... | ||
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``` | ||
No compiler found, expected minor version match with... | ||
Try running "stack setup" to install the correct GHC... | ||
``` | ||
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Just do as it says and it will download and install | ||
the correct compiler version: | ||
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```bash | ||
stack setup | ||
``` | ||
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## Running *GHCi* | ||
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If you want to play with your solution in GHCi, just run the command: | ||
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```bash | ||
stack ghci | ||
``` | ||
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## Feedback, Issues, Pull Requests | ||
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The [exercism/haskell](https://github.com/exercism/haskell) repository on | ||
GitHub is the home for all of the Haskell exercises. | ||
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If you have feedback about an exercise, or want to help implementing a new | ||
one, head over there and create an issue. We'll do our best to help you! | ||
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## Source | ||
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An unsolved problem in mathematics named after mathematician Lothar Collatz [https://en.wikipedia.org/wiki/3x_%2B_1_problem](https://en.wikipedia.org/wiki/3x_%2B_1_problem) | ||
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## Submitting Incomplete Solutions | ||
It's possible to submit an incomplete solution so you can see how others have completed the exercise. |
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exercises/collatz-conjecture/examples/success-standard/package.yaml
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name: collatz-conjecture | ||
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dependencies: | ||
- base | ||
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library: | ||
exposed-modules: CollatzConjecture | ||
source-dirs: src | ||
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tests: | ||
test: | ||
main: Tests.hs | ||
source-dirs: test | ||
dependencies: | ||
- collatz-conjecture | ||
- hspec |
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exercises/collatz-conjecture/examples/success-standard/src/CollatzConjecture.hs
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module CollatzConjecture (collatz) where | ||
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collatzHelper :: Integer -> Integer -> Maybe Integer | ||
collatzHelper t x | x == 1 = Just t | ||
| even x = collatzHelper (t+1) (x `div` 2) | ||
| otherwise = collatzHelper (t+1) (x*3 + 1) | ||
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collatz :: Integer -> Maybe Integer | ||
collatz x = if x <= 0 then Nothing else collatzHelper 0 x |
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name: collatz-conjecture | ||
version: 1.1.1.1 | ||
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dependencies: | ||
- base | ||
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library: | ||
exposed-modules: CollatzConjecture | ||
source-dirs: src | ||
dependencies: | ||
# - foo # List here the packages you | ||
# - bar # want to use in your solution. | ||
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tests: | ||
test: | ||
main: Tests.hs | ||
source-dirs: test | ||
dependencies: | ||
- collatz-conjecture | ||
- hspec |
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module CollatzConjecture (collatz) where | ||
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collatz :: Integer -> Maybe Integer | ||
collatz = error "You need to implement this function." |
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resolver: lts-8.21 |
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{-# OPTIONS_GHC -fno-warn-type-defaults #-} | ||
{-# LANGUAGE RecordWildCards #-} | ||
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import Data.Foldable (for_) | ||
import Test.Hspec (Spec, describe, it, shouldBe) | ||
import Test.Hspec.Runner (configFastFail, defaultConfig, hspecWith) | ||
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import CollatzConjecture (collatz) | ||
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main :: IO () | ||
main = hspecWith defaultConfig {configFastFail = True} specs | ||
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specs :: Spec | ||
specs = describe "collatz" $ for_ cases test | ||
where | ||
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test Case{..} = it description assertion | ||
where | ||
assertion = collatz number `shouldBe` expected | ||
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data Case = Case { description :: String | ||
, number :: Integer | ||
, expected :: Maybe Integer | ||
} | ||
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cases :: [Case] | ||
cases = [ Case { description = "zero steps for one" | ||
, number = 1 | ||
, expected = Just 0 | ||
} | ||
, Case { description = "divide if even" | ||
, number = 16 | ||
, expected = Just 4 | ||
} | ||
, Case { description = "even and odd steps" | ||
, number = 12 | ||
, expected = Just 9 | ||
} | ||
, Case { description = "Large number of even and odd steps" | ||
, number = 1000000 | ||
, expected = Just 152 | ||
} | ||
, Case { description = "zero is an error" | ||
, number = 0 | ||
, expected = Nothing | ||
} | ||
, Case { description = "negative value is an error" | ||
, number = -15 | ||
, expected = Nothing | ||
} | ||
] |